pcKbSkew: Principal-component-based Khattree-Bahuguna's Multivariate...
In KbMvtSkew: Khattree-Bahuguna's Univariate and Multivariate Skewness

Description Usage Arguments Details Value References See Also Examples

View source: R/KbSkewness.R

Compute Principal-component-based Khattree-Bahuguna's Multivariate Skewness.

1	pcKbSkew(x, cor = FALSE)

`x`	a matrix of original scale observations.
`cor`	a logical value indicating whether the calculation should use the correlation matrix (`cor = TRUE`) or the covariance matrix (`cor = FALSE`). The default value is `cor = FALSE`.

Let \mathbf{X} = X_1, …, X_p be a p-dimensional multivariate random vector. We compute the sample skewness for p principal components of \mathbf{X} respectively by the sample Khattree-Bahuguna's univariate skewness formula (see details of kbSkew that follows). Let η_1, η_2, …, η_p be the p univariate skewnesses for p principal components. Principal-component-based Khattree-Bahuguna's multivariate skewness for a sample is then defined as

η = ∑_{i=1}^{p} η_i.

Clearly, 0 ≤ η ≤ \frac{p}{2}.

pcKbSkew gives the sample principal-component-based Khattree-Bahuguna's multivairate skewness.

Khattree, R. and Bahuguna, M. (2019). An alternative data analytic approach to measure the univariate and multivariate skewness. International Journal of Data Science and Analytics, Vol. 7, No. 1, 1-16.

kbSkew for Khattree-Bahuguna's univariate skewness.

# Compute principal-component-based Khattree-Bahuguna's multivairate skewness

data(OlymWomen)
pcKbSkew(OlymWomen[, c("m800","m1500","m3000","marathon")])